Here too
For what it's worth, my home computer is a 15" MacBook Pro (Mid 2012) with both the NVIDIA GeForce GT 650M and the Intel HD 4000. I installed Warcraft III in the same fashion you did on this machine as it shipped to me with Mountain Lion pre-installed. To my delight, the game works perfectly. On my work computer, a 13" MacBook Air (Mid 2011) with just the Intel HD 3000, with the game installed, again, in the same fashion, I have the same problem you are having. I did a fresh installation of Mountain Lion on this machine and am running 10.8.3. Still experiencing the problem.
I'd like to think that when my MacBook Pro is running Warcraft III it isn't defaulting to the GT 650 given that the HD 4000 is more than enough to run that game, but I don't really have any way of verifying this for sure, and I guess it's irrelevant. Point is that I'm another Mac user with an Intel HD 3000 and I'm experiencing the same problem. Interestingly enough, I also own a Windows ultrabook, an Asus Zenbook UX31E with a Sandy Bridge Core i5 processor. Said machine, also has the Intel HD 3000, but it has Windows 7 and under Windows 7 with this exact hardware, Warcraft III runs fine without this issue.
Given this, I'm inclined to believe that it it, in fact, something to do with the OS X Intel HD driver. But given that Blizzard has all but abandoned Mac support for Warcraft III and that Apple, therefore, has no reason to have Intel tweak their driver for this graphics chipset for this chipset, we will not see a fix of any kind.
Still though, when I went to google this problem, this thread was the first hit and it was exactly the same problem I was having.